Such a wheel hub cover arrangement is known, for example, from U.S. Pat. No. 5,785,390, which is incorporated by reference herein. In order to be able to vent a vehicle shaft connected to the wheel hub and carry out pressure equalization, a venting bore is provided which is connected to the atmosphere via further openings in a closure part. In order to prevent splash water or dirt from penetrating into the wheel hub, a membrane is provided between the venting bore and the further openings, which membrane is intended to protect the cover volume from the ingress of undesired contaminants. Such an arrangement is very complicated to assemble and thus also expensive to manufacture. Moreover, a closure element exposed in such a way is not desired for design reasons.